What is ln(4e^{-6/100 t}) ?

The solution to ln(4e^{-6/100 t}) is 2ln(2)-(3t)/(50)

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simplify ln(4e^{-6/100 t})

simplify

ln (4 e^{- \frac{6}{100} t})

2 ln (2) - \frac{3 t}{50}

Solution steps

ln (4 e^{- \frac{6}{100} t})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (4 e^{- \frac{6}{100} t}) = ln (4) + ln (e^{- \frac{6}{100} t})

= ln (4) + ln (e^{- \frac{6}{100} t})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (e^{- \frac{6}{100} t}) = - \frac{6}{100} t ln (e)

= ln (4) - \frac{6}{100} t ln (e)

\frac{6}{100} t ln (e) = \frac{3 t}{50}

= ln (4) - \frac{3 t}{50}

ln (4) = 2 ln (2)

= 2 ln (2) - \frac{3 t}{50}

20 e^{9} + ln (12) + 50 - ln (9)

- lo g_{10} (2.3 \cdot 1 0^{- 9})

ln (\frac{1}{2 ^{n}} \cdot e^{- 2 x} e^{- 3 t})

\frac{3}{2} (lo g_{10} (4.94145) - lo g_{10} (761.21))

ln (\frac{r \cdot 0.04}{2.51})

What is ln(4e^{-6/100 t}) ?
The solution to ln(4e^{-6/100 t}) is 2ln(2)-(3t)/(50)